The motif problem

Fix a choice and ordering of four pairwise non-adjacent vertices of a parallelepiped, and call a motif a sequence of four points in R^3 that coincide with these vertices for some, possibly degenerate, parallelepiped whose edges are parallel to the axes. We show that a set of r points can contain at most r^2 motifs. Generalizing the notion of motif to a sequence of L points in R^p, we show that the maximum number of motifs that can occur in a point set of a given size is related to a linear programming problem arising from hypergraph theory, and discuss some related questions.Comment: 17 pages, 1 figur

Unusual temperature dependence of band dispersion in Ba(Fe(1-x)Ru(x))2As2 and its consequences for antiferromagnetic ordering

We have performed detailed studies of the temperature evolution of the electronic structure in Ba(Fe(1-x)Ru(x))2As2 using Angle Resolved Photoemission Spectroscopy (ARPES). Surprisingly, we find that the binding energy of both hole and electron bands changes significantly with temperature in pure and Ru substituted samples. The hole and electron pockets are well nested at low temperature in unsubstituted (BaFe2As2) samples, which likely drives the spin density wave (SDW) and resulting antiferromagnetic order. Upon warming, this nesting is degraded as the hole pocket shrinks and the electron pocket expands. Our results demonstrate that the temperature dependent nesting may play an important role in driving the antiferromagnetic/paramagnetic phase transition.Comment: 5 pages, 6 figure

Remarkably robust and correlated coherence and antiferromagnetism in (Ce1−x_{1-x}Lax_x)Cu2_2Ge2_2

We present magnetic susceptibility, resistivity, specific heat, and thermoelectric power measurements on (Ce$_{1-x}$La$_x$)Cu$_2$Ge$_2$ single crystals (0 $\leq x\leq$ 1). With La substitution, the antiferromagnetic temperature $T_N$ is suppressed in an almost linear fashion and moves below 0.36 K, the base temperature of our measurements for $x>$ 0.8. Surprisingly, in addition to robust antiferromagnetism, the system also shows low temperature coherent scattering below $T_{coh}$ up to $\sim$ 0.9 of La, indicating a small percolation limit $\sim$ 9$\%$ of Ce that separates a coherent regime from a single-ion Kondo impurity regime. $T_{coh}$ as a function of magnetic field was found to have different behavior for $x$ 0.9. Remarkably, $(T_{coh})^2$ at $H$ = 0 was found to be linearly proportional to $T_N$. The jump in the magnetic specific heat $\delta C_{m}$ at $T_N$ as a function of $T_K/T_N$ for (Ce$_{1-x}$La$_x$)Cu$_2$Ge$_2$ follows the theoretical prediction based on the molecular field calculation for the $S$ = 1/2 resonant level model

Unpaired Electrons in the Heavy-Fermion Superconductor CeCoIn_{5}

Thermal conductivity and specific heat were measured in the superconducting state of the heavy fermion material Ce_{1-x}La_{x}CoIn_{5}. With increasing impurity concentration x, the suppression of T_{c} is accompanied by the increase in the residual electronic specific heat expected of a d-wave superconductor, but it occurs in parallel with a decrease in residual electronic thermal conductivity. This contrasting behavior reveals the presence of uncondensed electrons coexisting with nodal quasiparticles. An extreme multiband scenario is proposed, with a d-wave superconducting gap on the heavy-electron sheets of the Fermi surface and a negligible gap on the light, three-dimensional pockets.Comment: 4 pages, 3 figure

Superconductivity in Dense MgB2MgB_2 Wires

$MgB_2$ becomes superconducting just below 40 K. Whereas porous polycrystalline samples of $MgB_2$ can be synthesized from boron powders, in this letter we demonstrate that dense wires of $MgB_2$ can be prepared by exposing boron filaments to $Mg$ vapor. The resulting wires have a diameter of 160 ${\mu}m$, are better than 80% dense and manifest the full $\chi = -1/4{\pi}$ shielding in the superconducting state. Temperature-dependent resistivity measurements indicate that $MgB_2$ is a highly conducting metal in the normal state with $\rho (40 K)$ = 0.38 $\mu Ohm$-$cm$. Using this value, an electronic mean free path, $l \approx 600~\AA$ can be estimated, indicating that $MgB_2$ wires are well within the clean limit. $T_c$, $H_{c2}(T)$, and $J_c$ data indicate that $MgB_2$ manifests comparable or better superconducting properties in dense wire form than it manifests as a sintered pellet.Comment: Figures' layout fixe

A Unique Exposure of Quaternary Deposits in Johnson County, Iowa

The Klein Quarry, in Johnson County, Iowa, exposes a unique section of Quaternary deposits. The section extends along the axis of a Late-Sangamon erosion surface. It is mantled by Wisconsinan loess: a 4-5m upper increment of Late-Wisconsinan loess and a thin increment (0.2 to 0.5m) of mixed loess and Wisconsinan-age pedisediment (\u27basal-loess sediments\u27). Some soil development has taken place in the basal-loess sediments (basal-loess paleosol), and this soil merges with the underlying Late-Sangamon Paleosol. The Late-Sangamon erosion surface is developed on Pre-Illinoian age deposits of the Wolf Creek Formation which include (from top to bottom) an upper basal till (the Aurora Till Member), a thin, laminated diamicton, and an underlying stratified fluvial sequence of sand, silt, and gravel. These overlie till of the Alburnett Formation which is locally preserved in low-relief sags on the underlying bedrock surface of Devonian Cedar Valley Limestone. Sedimentary structures, pebble fabrics, and stratigraphic relations suggest that: the stratified fluvial sequence originated as a proglacial fluvial outwash that evolved into a low-energy slackwater environment; the laminated diamicton was derived from glacial sediments which were resedimented and deposited in this slackwater environment; and this was followed by overriding of glacial ice and deposition of the basal till. The Late-Sangamon erosion surface is marked by a stone line and a relatively thin increment of associated pedisediment which overlies the stone line. Various hillslope components are exposed going down the Late-Sangamon paleohillslope. The erosion surface progressively truncates the Aurora Till Member, the laminated diamicton, and most of the stratified sequence of the Wolf Creek Formation. Properties of the stone line and pedisediment vary in a complex, but systematic way. The characteristics of the stone line and lowermost pedisediment vary downslope directly with textural variations in the different deposits underlying the erosion surface. The uppermost pedisediment, however, shows little relationship to the materials underlying the stone line. The upper, younger pedisediment has resulted from reworking older pedisediment and from transport of sediment from farther upslope. The greater transport distance and reworking results in greater sorting and a less direct relationship to local source materials. The Lare-Sangamon Paleosol formed on this paleohillslope, and is developed in the Late-Sangamon pedisediment, stone line, and the underlying Wolf Creek Formation deposits. Sedimentological variations in the pedisediment affect various paleosol properties. Thickness of the paleosol varies (1.8 to 2.3 m) directly with the thickness of pedisediment, becoming thicker down the paleoslope. The increase in paleosol thickness is also directly matched by an increase in B-horizon thickness. The pedologic and sedimentologic features indicate that the Late-Sangamon erosion surface - pedisediment - paleosol evolved slowly and systematically. Pedisediment muse have accumulated in the lower-slope positions at a slow enough rate that B-horizon soil development kept pace with sediment accumulation